Advances in micro and nanoengineered surfaces for enhancing boiling and condensation heat transfer: a review

Liquid–vapor phase change phenomena such as boiling and condensation are processes widely implemented in industrial systems such as power plants, refrigeration and air conditioning systems, desalination plants, water processing installations and thermal management devices due to their enhanced heat transfer capability when compared to single-phase processes. The last decade has seen significant advances in the development and application of micro and nanostructured surfaces to enhance phase change heat transfer. Phase change heat transfer enhancement mechanisms on micro and nanostructures are significantly different from those on conventional surfaces. In this review, we provide a comprehensive summary of the effects of micro and nanostructure morphology and surface chemistry on phase change phenomena. Our review elucidates how various rational designs of micro and nanostructures can be utilized to increase heat flux and heat transfer coefficient in the case of both boiling and condensation at different environmental conditions by manipulating surface wetting and nucleation rate. We also discuss phase change heat transfer performance of liquids having higher surface tension such as water and lower surface tension liquids such as dielectric fluids, hydrocarbons and refrigerants. We discuss the effects of micro/nanostructures on boiling and condensation in both external quiescent and internal flow conditions. The review also outlines limitations of micro/nanostructures and discusses the rational development of structures to mitigate these limitations. We end the review by summarizing recent machine learning approaches for predicting heat transfer performance of micro and nanostructured surfaces in boiling and condensation applications.

Nithin Vinod Upot is a PhD candidate in the Mechanical Science and Engineering department at the University of Illinois at Urbana-Champaign (UIUC) and is a member of the Energy Transport Research Lab (ETRL). He received his Bachelor's degree in Mechanical Engineering from the College of Engineering Guindy (CEG) in 2014 and a Master's degree in Aerospace Engineering from UIUC in 2016. His research work focuses on refrigerant-side ow boiling enhancements through the creation of scalable micro/ nanostructures. His research interests also include thermal management for electronics cooling, both at the system-level and die-level.
Kazi Fazle Rabbi received his Bachelor's degree in Mechanical Engineering (summa cum laude) from the Bangladesh University of Engineering and Technology in 2016 and received his PhD in Mechanical Science and Engineering from UIUC in 2022 where he worked in the Energy Transport Research Lab. He is currently a Senior Technology Development Engineer in Intel Corporation. His research interests include phase change heat transfer enhancement utilizing functionalized surfaces, thermal management of electronics, anticorrosive thin lm coatings for thermal application and surface frosting/icing mitigation.

Introduction
Nanoengineered surfaces are at the forefront of next generation energy-efficient thermal management systems due to their immense potential to enhance phase change heat transfer. In particular, the presence of surface microstructures (structure characteristic length scale >1 mm) and nanostructures (structure characteristic length scale <1 mm) have the potential to alter surface chemistry and signicantly inuence solid-liquidvapor interfacial dynamics to radically promote phase transition. Amongst the various phase change modes, liquid-vapor phase transitions, i.e., boiling and condensation, are the most widely implemented in industrial systems such as in steambased power plants, 1 refrigeration cycles, 2 seawater desalination installations, 3 thermal management devices for electronics, 4-10 and electried transportation. [11][12][13] Condensation occurs when vapor is converted to liquid by latent heat removal as it meets a subcooled surface. The introduction of functionalized micro/nanostructures enables the realization of discrete droplet formation during condensation (also known as dropwise condensation 14 ) which is characterized by high heat removal rates as opposed to the conventional lmwise condensation mode which faces a fundamental limitation of the high thermal barrier imposed by conduction through the condensate lm. [15][16][17] Recently, the discovery of novel jumping droplet condensation mechanisms 18-20 on micro and nanostructures that fundamentally differ from conventional dropwise condensation on smooth promoter coatings [21][22][23] have also spurred renewed research interest. Similarly, boiling, a process of liquid-to-vapor conversion latent heat supply and Siavash Khodakarami is a PhD student in the Mechanical Science and Engineering department at UIUC and a member of Energy Transport Research Lab (ETRL). He received his M. S. in Mechanical Engineering from UIUC in 2021. His research focuses on twophase heat transfer characterization on engineered surfaces using data-driven modeling and machine vision techniques to capture and predict the dynamics of droplets/bubbles and developing new cost-effective reliable two-phase heat transfer methods using machine learning. bubble nucleation, growth and departure on a heated surface, can also be enhanced by the addition of micro and nanostructures on the boiling surface. These structures not only provide cavities of appropriate length-scale to activate bubble nucleation which improves heat transfer coefficient (HTC), but they also demonstrate potential to enable surface self-rewetting which delays the occurrence of the undesirable critical heat ux (CHF), a hydrodynamically unstable state.
Owing to the promising demonstration of micro/ nanostructures to enhance boiling and condensation and their potential for improvements in two-phase system efficiency, extensive studies in the eld of phase change heat transfer have been conducted resulting in a large collection of experimental data. Many variations of micro-and nanoengineered surfaces (estimate to be as high as 1000) have also been introduced and characterized for a variety of substrates and materials. A review of the micro/nanostructure morphologies and their related thermal performance is, therefore, essential not only to identify better-performing structure morphologies and to ascertain the potential phase change mechanisms within these structures, but also to identify existing research gaps and important works that need to be conducted. Furthermore, considering the rapid advancements in nanofabrication in recent years, it is also timely to review and assess the recent micro and nanoscale visualization techniques implemented in phase change heat transfer applications and the new transport phenomena uncovered.
In this review, we discuss recent progress in micro/ nanostructure enhanced boiling and condensation heat transfer by focusing on the inuence of surface morphology on the transport mechanisms of heat and mass. Key thermal performance indicators such as boiling/condensation HTC, condensate ooding and boiling CHF of the various micro/ nanostructured surfaces shall be collated and analyzed. We hope that through this review, we can identify rational approaches to modifying surface wettability through implementation of micro/nanostructures to enhance HTC and CHF under both quiescent and ow conditions. Existing reviews on boiling/condensation heat transfer focus on overall surface engineering such as micro/nanostructuring or wettability modication of smooth as well as structured surfaces for enhancing condensation and boiling. [24][25][26][27] Unlike past reviews, this review not only covers the material development aspect of enhanced surfaces, but it also presents in depth discussion regarding the synergistic interaction of bubbles/droplets and structures and their inuence on boiling/condensation mechanisms such as microscopic bubble/droplet growth dynamics and three-phase contact line evolution. When compared to previous reviews, [24][25][26][27] both for boiling and condensation enhancement, we include sections focusing on non-ow (quiescent) conditions as well as ow conditions, where we discuss how different design of micro/nanostructured surfaces can be utilized for each specic condition. Apart from the commonly used uids such as water, here the effectiveness of micro and nanostructured surfaces in promoting boiling and condensation of liquids having various surface tension i.e., water, hydrocarbons and refrigerants commonly used in industry, are critically evaluated. Despite the development of a plethora of micro and nanostructures over the last decade, many surface fabrication methods are not scalable. Furthermore, the majority of surface micro/nanostructures are susceptible to degradation and surface contamination which prevents their implementation in long term commercial and industrial applications. Our review discusses potential applications and guidelines for scalable and durable implementation of micro/nanostructures at the industrial level. Furthermore, considering recent interest in machine learning application to predict phase change heat transfer performance, we include analysis and discussion of available machine learning approaches for both boiling and condensation applications.

Pool boiling
The boiling curve for saturated pool boiling, a plot of heat ux against wall superheat, is shown in Fig. 1A. 28 The region o-a corresponds to heat transfer by natural convection with no bubbles being formed. At point a, bubbles begin to form once the wall superheat has been raised to a sufficiently high level and this point is known as the onset of nucleate boiling (ONB). For highly wetting uids which exhibit low surface tension, the ONB could be delayed to point a ′ and is typically followed by numerous cavities being activated together which leads to a reduction in wall superheat at the same heat ux condition (region a ′ -a). Nucleate boiling begins from point a aer ONB and isolated discrete bubbles control heat transfer in the initial region of nucleate boiling on increasing heat ux (a-b). Further increase in heat ux leads to activation of more nucleation sites and generation of more bubbles with bubble coalescence being observed. This region (b-c) is characterized by vapor columns with high heat transfer coefficients being exhibited in the fully developed nucleate boiling portion of the boiling curve. It is important to note that while the existence of vapor columns have been postulated in early pool boiling models, physical observation of such columns remain scarcely reported and is a topic that needs to be studied further. 29 Continuous increase of heat ux will eventually lead to periodic dry patches being formed on the heater surface which are rewetted by the surrounding liquid (c-d) and this in turn leads to a reduction in the slope of the boiling curve which translates to reduction in heat transfer coefficients. Once the heater surface is covered with a vapor blanket, liquid is unable to rewet the surface and this point is known as the critical heat ux (CHF). The wall temperature drastically increases and can lead to heater burnout depending on the material. The region e-f corresponds to lm boiling where the surface is covered with vapor without any liquid in direct contact and can be attained by reduction of heat ux. The region d-e in between nucleate boiling and lm boiling regions is known as the transition region and is very unstable.
Since the nucleate boiling portion of the pool boiling curve results in the highest heat transfer coefficients, most applications involving pool boiling tend to focus on operation in this region. Within nucleate boiling, heat transfer primarily occurs through three modes: (1) microlayer evaporation, (2) transient conduction, and (3) microconvection. Microlayer evaporation refers to heat transfer due to evaporation of liquid underneath the growing vapor bubble and the interface of the vapor bubble. Transient conduction occurs as the liquid front advances to rewet the dry patch, while microconvection refers to heat transfer caused by disturbance of liquid layer adjacent to departing bubbles. Microlayer evaporation leads to eventual formation of dry spots on the heater surface and surrounding liquid rewets the surface leading to heat transfer due to transient conduction from the heater surface and microconvection. The relative contributions of the components of the bubble ebullition cycle have been investigated in the past, 30-32 with many previous studies focused on microlayer evaporation contribution. [33][34][35] Fig. 1B and C displays the microlayer evaporation contribution and transient conduction/microconvection contribution during saturated pool boiling of FC-72 obtained with microheaters. The microlayer evaporation component was found to contribute up to 20% to the total heat transfer while the transient conduction and microconvective components dominate. While similar trends have been reported in other studies as well, 36,37 well developed understanding of each of these three regions is essential for future pool boiling work.

Mechanisms governing micro/nanostructure enhanced heterogeneous pool boiling
In heterogeneous pool boiling, bubbles grow from pre-existing vapor embryos trapped in the cavities of a heated surface. The mechanisms driving bubble growth not only depends on the surface thermal conditions but also on the presence of suitable cavity size range for vapor entrapment and growth activation. By considering transient thermal boundary layer development during the bubble ebullition cycle, existing models have showed that bubble nucleation takes place only in submicron and micron scale cavities and the actual size range depends on the uid properties such as surface tension and latent heat of vaporization. [38][39][40] For instance, active bubble nucleation sites typically require the surface cavity radii to range between 0.01 and 1 mm for water, 41 whereas for signicantly lower surface tension and latent heat uids such as dielectric uids, cavity radii of 0.03 to 50 mm are found to be more desirable. 42 While conventional unstructured "smooth" surfaces possess inherent cavities formed through the manufacturing process, the cavity sizes are undesirable for bubble nucleation resulting in high boiling incipience temperature and limited heat transfer. 43 In this regard, surface micro/nanoengineering has the potential to the generate suitable surface cavities to increase nucleation size density for pool boiling enhancements and have received increasing attention in the last few decades. [44][45][46][47] Furthermore, the wall superheat required for onset of nucleate boiling (ONB) has been shown to decrease with engineered nucleation sites, 48 thus expanding the region of nucleate pool boiling and increasing HTC.
In addition to increasing the number of active nucleation sites, cavity geometry parameters such as width and depth also play an important role in improving heat transfer. A decrease in ONB superheat with increasing cavity depth and increased nucleation leading to HTC enhancements of 150% has been reported. 49 However, an increase in cavity depth can also lead to smaller enhancements due to increased resistance to liquid replenishment, which in turn leads to heat transfer degradation, 50 thus implying a non-monotonous relationship of cavity depth with heat transfer enhancements. Cavity sizing and cavity spacing are two other important characteristics to be considered when designing micro/nanoengineered surfaces. For instance, while increasing nucleation site density increases HTC due to higher bubble generation, this also leads to the overcrowding of bubbles on the heated surfaces which coalescences to form large vapor mushrooms and early occurrence of CHF. 51 It has been shown that an increase in microcavity diameter along with a decrease in spacings between microcavities can lead to the undesirable effect of bubble overcrowding and reduce CHF. 52 To overcome this issue, surfaces can be designed to enable differentiated bubble departure and liquid replenishment pathways, minimizing the resistance to bubble removal and facilitating rewetting of the heated surface. 53 Also known as separation of liquid-vapor pathways, this approach is commonly adopted to enable HTC and CHF coenhancement. [54][55][56] Instead of having surfaces uniformly coated with micro/nanostructures, hybrid surfaces consisting of structured and plain regions are an effective strategy to facilitate separated liquid-vapor pathways. 57,58 Biphilic surfaces can have increased heat transfer coefficients when compared to surfaces with uniform wettability due to efficient liquid and vapor transport. 59 Furthermore, the creation of cavities of appropriate size can tune the bubble departure direction, i.e., whether bubbles escape from top or side, relative to bubble departure diameter. 53 Apart from increasing nucleation site density, micro/ nanocavities also induce capillary force on the surrounding liquid which facilitates the timely replenishment of liquid to its surface. Hence, the capillary wicking mechanism has shown the potential to signicantly increase CHF. 60 To improve heat transfer performance and delay CHF, the micro/nanostructure morphology and length scale play a pivotal role to optimize the interplay between capillary pressure and permeability. 61 Innovative designs such as porous biomimetic structures, 62 metal organic framework-based surfaces, 63 and fractal surfaces 64,65 have all been shown to demonstrate signicant CHF enhancements due to enhanced capillary action. Enhanced capillary action leading to increased bubble departure frequency can also improve performance. 66 To investigate capillary-action attributed enhancements in detail, well-ordered microporous wick structures were designed and investigated ( Fig. 2A and B). 67 CHF in these porous wicks depends on the capillary limit, dened as the ability of the liquid to wet the surface, as well as the boiling limit, dened as the ability of the liquid to rewet the surface aer vapor extraction. While a reduction in wicking length leads to enhancement in CHF in the capillary limit, reduction below a certain limit can lead to transition to the boiling limit where CHF enhancements were no longer observed (Fig. 2C). Similar transition effects are also observed on increasing structure thickness beyond an optimum wick thickness. While numerous boiling CHF models for unstructured surfaces have been developed, 68-70 similar models for structured surfaces remain scarce. A unied model combining the effects of surface roughness and wicking has been shown to give good results and can be utilized to guide design. 71 Extreme boiling enhancements can be realized by combining the abovementioned enhancement mechanisms of increased nucleation sites, optimum cavity geometry and capillary wicking. 72 Heat transfer coefficient enhancements of 389% and CHF enhancements of 138% have been recently reported on a three-tier hierarchical tube-cluster in pillar (h-TIP) surface. This strategy enables increased nucleation via micron-scale cavities, enhanced capillary action/evaporation through nanostructures and minimal bubble coalescence via well-spaced tube clusters (Fig. 2D). The tube cluster spacing approach counters the issue of increased bubble coalescence typically seen on surfaces with increased nucleation sites, leading to simultaneous enhancements in CHF and HTC.

Effect of surface wettability and uid surface tension on pool boiling
The effect of surface wettability on pool boiling performance has been widely examined. [74][75][76] The nucleation rate during pool boiling is signicantly dependent on surface wettability. 77 Hydrophobic surfaces exhibit higher bubble nucleation sites due to the presence of the non-wetting spots, enabling the entrapment of vapor embryo. 78 The effect of altering surface wettability to produce superhydrophilic surfaces (via structured surfaces) on boiling performance with water as the working uid has been another focus area gaining traction past few years in terms of experimental studies. 79 Nickel inverse-opal structures transitioning from hydrophilic before boiling to hydrophobic within a few minutes aer boiling showcases an example where altered wettability is naturally achieved. 52 Arti-cial cavities on a silicon surface having a Teon coating applied to impart hydrophobicity have shown differing bubble coalescence characteristics for hydrophilic and hydrophobic surfaces (Fig. 3A). 67 Hydrophilic surfaces primarily demonstrate  73 The boiling CHF decreases after the liquid wicking length increases beyond a critical value, suggesting a transition from the boiling limit regime to the capillary limit regime. d p refers to pore diameter while d n refers to neck diameter. Reproduced with permission from ref. 73 horizontal bubble coalescence while hydrophobic surfaces show vertical bubble coalescence ( Fig. 3B and C). Hydrophobic surfaces were found to perform better due to increased departure frequency caused by increased bubble coalescence. Residual vapor le behind on the hydrophobic surface aer bubble coalescence leads to a reduction in waiting time for the next bubble nucleation event, thereby enhancing heat transfer. Superhydrophobic surfaces can also enable nucleation at lower wall superheat when compared to superhydrophilic surfaces. 80 However, vapor agglomeration resulting from bubble coalescence and larger surface tension forces preventing bubble detachment on superhydrophobic surfaces can also hinder heat transfer at moderate and high heat ux when compared to superhydrophilic surfaces and thus, care needs to be taken while utilizing such substrates.
Pool boiling enhancements with low-surface tension working uids, such as dielectrics and refrigerants, have been demonstrated via structured surfaces such as copper spherical granules, 1 silicon dioxide thin lm nanocoated surfaces 81 and zinc-oxide nanowires. 82 Heat transfer coefficient enhancements up to 200% demonstrated with commercial nanoFLUX coatings utilizing R-134a and R-245fa have primarily been attributed to increased nucleation sites, increased capillary pumping, and enhanced evaporation of wicked liquid beneath growing vapor bubbles. 83 The interesting phenomena of decreased wall superheat on increasing heat ux, termed 'hookback', has been shown with FC-72. 84 This is caused due to simultaneous activation of numerous submicron cavities and has been found to be dependent on the level of subcooling and the size-range of cavities. Since capillary wicking for low-surface tension uids is lower than high surface-tension uids such as water, the role of pre-existing liquid also plays an important role in addition to capillary wicking for CHF enhancement with low surface tension working uids. 85

Pool boiling visualization techniques
Observation of bubble growth and departure are critical in furthering our understanding of fundamental boiling characteristics and bubble dynamics. Most studies thus far have employed high-speed camera imaging to determine fundamental parameters of importance for boiling. 86,87 Reentrant cavity surfaces have received signicant attention in the past and have been shown to induce earlier onset of nucleate boiling when combined with porous surfaces ( Fig. 4A and B). These surfaces have been shown to increase heat transfer coefficients up to 500% at low and moderate heat ux conditions due to an increase in nucleation sites and rewetting. 88,89 Imaging outside the working tool has enabled characterization of the bubble ebullition cycle with bubble nucleation, growth and departure being captured ( Fig. 4C-F). Effects of subcooling on bubble nucleation have been demonstrated with a graphene oxide nanocoating on plain copper surface. 90 Smaller bubble departure diameters on increasing subcooling led to delays in bubble coalescence and thereby increased critical heat ux. While such visualization techniques have contributed signicantly to boiling studies, they only provide far-eld visualization of the boiling phenomenon. Due to resolution limitations, these techniques are unable to reveal details of the bubble evolution and interaction at the three-phase contact line during microscopic level examination. Recent studies have utilized high resolution techniques to overcome these limitations. Infrared imaging and endoscopic visualization are two such visualization techniques that have gained traction over the past few years, and we focus our attention on these two techniques.
Infrared (IR) imaging techniques have been utilized in the wall heat ux partitioning approach to determine local heat ux during pool boiling. While empirical correlations for determination of heat ux have been widely used in the past, 91-95 the partitioning approach has also been shown to perform well. 96 The local heat ux in pool boiling has generally been understood to be composed of three parts: (1) convective heat ux, (2) quenching/transient conduction heat ux, and (3) evaporative heat ux. IR imaging can enable extraction of bubble parameters such as size, frequency, nucleation site density, waiting time and these parameters can then be incorporated into the heat ux partitioning model. 97 Inclusion of parameters such as roughness ratio to account for the area increase in microstructured surfaces have been demonstrated to give good predictions for structured substrates as well. 98 Similar heat ux partitioning models have also been developed for subcooled and nucleate ow boiling. [99][100][101] Microlayer temperature distribution has also been obtained with IR thermography. 102 Highspeed imaging and IR thermometry have been used in conjunction to estimate bubble parameters with observations of bubble radius, microlayer radius and dry out radius showing good agreement with prior models. 103 The characteristic temperature response under a growing bubble which then departs has also been reported (Fig. 5A), 104 showcasing the slow heating and rapid cooling process before and aer bubble departure. Similar IR imaging techniques have also been applied with nanouids, where a reduction in bubble departure frequency and nucleation site density led to a 50% reduction in HTC when compared to water. 105,106 IR imaging has been utilized to determine temperature distributions during boiling on a 50 mm thick zirconium foil ( Fig. 5B-D). 107 The importance of substrate thickness during boiling has been reported in this study with the absence of dry spot formation at bubble base for thin metallic foils, which contrasts with the behavior seen for substrates with larger thickness. This leads to lower evaporative heat ux contribution with similar convective and quenching contributions to the local heat ux. A combination of particle image velocimetry and IR thermometry has recently shown possible links between uid ow and heat transfer during pool boiling. 108 Two color laser induced uorescence was used to track uid ow while IR thermometry was utilized to obtain temperature distribution. Results showed formation of vortices on the sides of rising bubbles led to mixing close to the heater with IR imaging showing lower temperatures at nucleation sites. 109 IR imaging has also been utilized to detect liquid/vapor phases in contact with the substrate during boiling and for determination of the wetted are fraction. 110 This methodology relies on the difference in IR intensity with higher intensity being observed for liquid regions and lower intensity for bubble regions. 111 Recently, a new technique of utilizing endoscopic visualization inside the work pool has overcome the existing limitation of far-eld visualization. Hierarchical copper structures ( Fig. 6A) having high wickability were shown to demonstrate enhancements over a period of 1 year, thus demonstrating durability. 112 Endoscope characterization showed the presence of retained liquid lm in addition to the microlayer for the hierarchical surface (Fig. 6B). This retained lm is gradually replaced by the dry area aer 375 days, aer which the surface loses it wicking potential, signied by disappearance of wicking front (Fig. 6C) due to adsorption of hydrophobic volatile organic compounds (VOCs) from air. Endoscopic observations have also enabled denition of a new dimensionless number, retention no. (Ret), which is the ratio of evaporated mass ux of liquid retained within structures to mass ux of vapor leaving the surface due to complete evaporation. 113 The CHF is found to vary linearly with Ret and experiments performed with surfaces having similar wickability but different water content showed Ret being a better predictor of CHF than wickability. The proposed retention number based CHF model is particularly important for structured surfaces without any interconnected pores where the effects of wickability are negligible. Such endoscopic visualization studies have also aided in determining a linear relationship between bubble departure diameter and CHF 114 and identication of a wicking area between the dry spot and microlayer region in novel metallic microchannels. 115 To understand fundamental physical phenomena driving boiling performance, many other innovative methods have also been demonstrated in recent studies. One such example is the usage of temperature sensitive paint to measure wall temperature distribution. 116 This technique enables simultaneous measurement of both wall temperature distribution and gasliquid interface, and thus could potentially be used in future studies as well. Additionally, MEMS sensors have also been widely employed for surface temperature measurement due to high-resolution capabilities. 30,36,117,118 Thus, technological advancements have facilitated development of a wide variety of high-resolution techniques and future boiling studies can be performed in conjunction with such devices instead of solely relying on traditional thermocouple/RTD measurements.

Flow boiling
The mechanisms governing ow boiling heat transfer are more complex than pool boiling due to the increased importance of forces such as buoyancy and inertia. Inertia, surface tension, shear, buoyancy, and evaporation momentum forces are signicant for ow boiling with varying relative values for these forces for microchannels and macrochannels. 119 Fig. 7 depicts the ow boiling process with various ow regimes for subcooled-inlet conditions. Single-phase liquid enters the tube and upon incrementing heat ux values, the wall superheat reaches a sufficiently high value for activation of nucleation sites and onset of nucleate boiling. At low vapor qualities, bubbly, slug, and stratied ow are typically observed while annular ow is observed at high vapor qualities. On increasing the heat ux to a sufficiently high value, partial dry-out of the tube wall begins followed by complete dry-out characterized by signicantly higher wall temperatures.  Flow boiling heat transfer has primarily been categorized as nucleate boiling dominant or convective boiling dominant depending on the relative effects of heat ux and mass ux. Increased effects of heat ux on the heat transfer coefficient with negligible mass ux effects have been indicative of nucleate boiling dominance, 121-125 while increased effects of mass ux and negligible effects of heat ux on heat transfer coefficients are considered to signify convective boiling dominance. [126][127][128] Heat transfer coefficients typically decrease as the vapor quality increases in nucleate boiling dominant regimes due to suppression of bubbly and slug ow along the tube length. On the other hand, convective boiling dominance results in the heat transfer coefficient increasing across vapor qualities due to enhanced evaporation from the progressively thinner liquid lm surrounding tube wall. 129 Previous studies have also shown nucleate and convective boiling effects to coexist with neither mechanism demonstrating dominance. [130][131][132][133] These relative effects of nucleation and convection have also formed the basis for a vast majority of ow boiling correlations to predict heat transfer coefficients. Three broad categories for correlations can be dened as follows: (1) superposition models, (2) asymptotic models, and (3) statistical models. Superposition models consist of two terms with each term quantifying the relative weight of nucleation and convection in the ow boiling process. 94,[134][135][136] The nucleation term consists of a nucleate pool boiling heat transfer coefficient correlation and a suppression factor to account for ow boiling. The convection term consists of a single-phase heat transfer coefficient and an enhancement factor to account for two-phase ow. Asymptotic models select one of the two mechanisms based on their absolute values since the heat transfer coefficient is considered to approach nucleate or convective boiling dominance, 137,138 while statistical models rely on tting experimental data to a range of non-dimensional numbers. 121,123,130,139 The importance of vapor quality has also been highlighted in a correlation proposed by Lee and Mudawar 140 with nucleate boiling dominating at low vapor qualities (x < 0.05) and convective boiling dominating at higher vapor qualities (x > 0.05).
In addition to empirical correlations, physics-based models have also been proposed for heat transfer coefficient prediction. While such mechanistic models are far fewer in number (when compared to empirical correlations) due to the complex nature of ow boiling, they reveal important physical characteristics not captured by correlations. Jacobi and Thome 141 proposed a two-zone heat transfer model (liquid slug and elongated vapor bubble) for microchannels with lm evaporation being considered the dominant mechanism. Thome et al. 142 extended on this work with a three-zone model where a vapor slug was added to the two earlier proposed zones and a cyclic passage of liquid slug, elongated bubble and vapor slug were considered to predict local heat transfer coefficient. An updated version of the three-zone model has recently been proposed by Magnini et al. 143 with liquid lm thickness being determined by accounting for bubble proximity effects and bubble nose velocity being calculated by capillary ow theory. Qu and Mudawar 144 proposed a model to determine the liquid lm thickness by considering liquid droplet entrainment in the vapor core and the heat transfer coefficient for microchannels was then determined by dividing the liquid thermal conductivity and lm thickness.

Nucleation sites, turbulence, and instability suppression
Flow boiling heat transfer mechanisms are governed by two distinct phenomena: (1) nucleate boiling contribution attributed to bubble growth and departure at low vapor qualities and (2) convective boiling contribution attributed to liquid lm evaporation at intermediate-high vapor qualities. 129 Heat transfer characteristics are highly dependent on surface morphology and can lead to efficient heat transfer by tuning nucleation site geometry and pore density. 145 Graphene based nanocomposite coatings on copper substrates have proven to be an effective method to increase pore density, thereby increasing nucleate boiling contribution. 146 Variation of coating concentration can increase pore density and further improve thermal performance. Similar effects of increased pore density (caused due to increased current density) leading to enhancements have been observed with Cu-Al 2 O 3 nanocomposite coatings on copper 147 and Cu-TiO 2 micro/nanostructured surfaces. 148 A reduction in static contact angle with increased porosity resulting in enhanced bubble departure frequency can give further enhancements.
An important consideration when considering utilization of coatings for performance enhancements is the effect of coating thermal conductivity on overall performance. Coatings with high thermal conductivity can improve performance. 146 Interconnected pores formed through structure fabrication also leads to enhanced wicking 149,150 and can increase lm evaporation contributions as well as bubble departure frequency. A laser-induced uorescence technique with 1 mm diameter tracer particles has been used to characterize liquid velocity inside pores. 151 Like pool boiling, the presence of numerous nucleation cavities also facilitate lower wall superheat ONB when compared to unstructured surfaces. 152 Higher HTC values at low mass uxes have been attributed to enhanced nucleation activity and lm evaporation with microporous copper surfaces. 153 Furthermore, porous inserts have shown enhancements at low heat ux values where the effects of convective boiling are more dominant without showing any signicant enhancements at high heat ux values. 154 This underlines the importance of structure characteristics and the need to perform detailed characterization studies to distinguish between various enhancement mechanisms.
Wall structures can also lead to disruptions in the boundary layer and cause perturbations in the liquid-vapor interface, promoting mixing and thereby enhancing heat transfer. 155 Flow boiling instabilities oen occur in mini/microchannel heat sinks and are generally characterized by increased pressure drop and wall temperature uctuations. 156 Dynamic instabilities such as bubble clogging in conned spaces can lead to ow reversal in microchannels. Onset of such instabilities during ow boiling are dependent on parameters such as channel geometry and operating conditions with larger inlet subcooling oen associated with faster occurrence of this phenomenon. [157][158][159] Vapor generation in microchannels has been shown to cause pressure drop uctuations in rectangular parallel microchannels as well. [160][161][162][163] Thus, ow boiling instabilities in microchannels can hurt enhancements that would otherwise be expected by creation of micro/nanoscale features on the base substrate and needs to be factored in while reporting results for better comparison between studies. Recent work has aimed at reduction of such instabilities with a biporous heat sink design sintered with copper woven tape being shown to reduce pressure drop uctuations. 164 An innovative 3D manifold microchannel design integrated with silicon nanowires has been shown to reduce these uctuations considerably. 165 While the top manifold enables vapor escape, the bottom microchannel exhibits enhanced thin lm evaporation via enhanced capillarity through interconnected nanocavities. In addition, surface wetting shis from being hydrophilic before tests to hydrophobic aer tests leading to degradation in performance at high mass ux/heat ux operating conditions where capillarity would otherwise have led to enhancements. While pressure oscillations are almost always accompanied by deterioration in HTCs, a recent study has reported heat transfer enhancements utilizing a copper wire mesh screen. 166 Peak pressure uctuations coincided with peak HTC enhancements and bubble burst caused by intense bubble activity was observed with nucleate boiling dominance for all heat ux values tested. Herringbone microns have shown to improve heat transfer performance during ow boiling. Annulus herringbone HTC enhancements up to 2.5 times of a plain surface have been made possible largely due to enhanced turbulence. 167,168 Similar enhancements have also been shown for enhanced structures inside tubing with refrigerants as the working uid. 169 The presence of additional nucleation sites and gas-phase shear resulting in enhanced mixing led to performance improvements. Higher HTC values at higher mass ux are caused due to a thinner liquid lm surrounding the tube wall, leading to lower conduction resistance and enhanced lm evaporation.
Hysteresis effects have been reported for hydrophilic surfaces where the HTC is not found to be the same when going from lower vapor quality to higher vapor quality and vice versa. An approximately 20% increase in HTC at low mass ux values was seen in carbon ber reinforced matrix with R-245fa when tests progressed from higher to lower vapor quality due to vapor lled nucleation cavities getting activated when liquid rewets. 170 Recent work incorporating micro-pin n fences aimed at rectifying chaotic ow regimes in silicon microchannel ow boiling has enabled efficient heat transfer performance. 164 These micro-pin fences are designed along the sidewalls with geometry parameters that enable wavelengths lower than the Kelvin-Helmholtz (KH) instability number (Fig. 8A). Presence of a single ow regimestable annular owleads to highly efficient thin lm evaporation that results in heat transfer performance close to the physical limit of boiling ( Fig. 8B and C). The superhydrophilic fences avoid the issue of entrained droplets within the vapor core and have also been shown to work with a low-surface tension uid (HFE-7100), where such enhancements are much more difficult to obtain due to the lower KH number. Micro-pin n fences also demonstrate lower wall temperature uctuation due to the stable annular ow. 171 Building on this work, silicon nanowire pin n fences enable even better performance when compared to micro-pin n fences due to higher capillary pressure. 172 This is seen in the exit vapor quality being 15% higher than that of micro-pin n fence boiling for constant temperature boundary conditions. Furthermore, a 43% reduction in pressure drop was also been reported due to enhanced rewetting. Microporous decorated sidewalls also rely on the mechanism of liquid-vapor separation for ow boiling enhancements and show an exit vapor quality of 0.3 compared to 0.1 for plain wall microchannels, signifying more efficient boiling. 173 Research with dielectric uids as the working uid in microchannels has gained prominence due to their usage in electronics cooling applications. 174 Additive manufacturing techniques such as Selective Laser Melting (SLM) have been employed to fabricate 3D porous metallic structures with FC-72 as the working uid. 175 Fractal hydrophilic networks have also demonstrated up to 82% CHF enhancement due to enhanced wetting through networks. 176 Application of piranha pin ns with HFE-7000 have demonstrated ultra-high cooling capabilities as well. 177 While PDMS based microchannels can be a good alternative to conventional silicon microchannels for exible electronic systems, poor thermophysical properties associated with such devices lead to less than satisfactory heat transfer performance. To overcome this limitation, PDMS wick structures with separate vapor removal pathways have been designed. 178 Such micropillars enable high capillary pressure and high permeability enabling stable liquid lm evaporation characterized by stable wall temperatures at high heat ux operating conditions. Phase separation and improved global liquid supply allow CHFs to approach those observed on silicon and copper microchannel heat sinks. Another innovative design with HFE-7100 as the working uid involved fabrication of microporous structures in wavy microchannels resulting in ∼60% HTC enhancement and ∼28% CHF enhancement when compared to straight microchannels (Fig. 9A). 179 Improvements in the nucleate boiling regime are caused due to increased nucleation sites and higher bubble detachment rate driven by centrifugal acceleration, while improvements in the lm evaporation regime are due to thinner liquid lm facilitated by the wavy channel (Fig. 9B). Heat transfer coefficients are independent of mass ux in the nucleate boiling zone while mass ux plays a role in the thin lm evaporation zone. Increased bubble nucleation and growth in the wavy concave region of the microchannel presents opportunities to further enhance HTC by increasing the wavy concave curvature and reducing wavy convex regions. Application of porous coatings in microchannels have also shown enhanced heat transfer coefficients with HFE-7200. 42 Creation of cavities in the desired range (0.6 to 3 mm) led to enhanced nucleation at low vapor qualities which resulted in peak HTC enhancement at a heat ux where bubbly ow and slug ow were found to dominate. In terms of local heat transfer characteristics, a sharp peak at low vapor qualities was followed by a gradual decline, representative of nucleate boiling suppression. At high vapor qualities, enhanced mixing led to heat transfer coefficient improvements despite nucleate boiling suppression. Early dry out for low mass ux while greater nucleate boiling suppression at highest mass ux led to highest average HTC enhancements at the intermediate mass ux.

Effect of micro/nanostructure wettability on ow boiling
Investigation of surfaces with heterogenous wettability has involved varying spacing between cavities and trials of varying shape patterns. [180][181][182] Amongst the shapes investigated, triangular shaped patterns were found to have the highest bubble liing force, which led to HTCs. Narrow inter-spacing between cavities led to premature bubble coalescence which prevented liquid replenishment and deteriorated heat transfer. Lower ONB superheats for structured surfaces in ow boiling are caused due to presence of additional cavities. The combination of hydrophobic coatings on a hydrophilic substrate has dual advantages: (1) corners formed between these varying wettability surfaces serve as nucleation sites forming nanoscale bubbles and (2) hydrophilic regions supply liquid facilitating bubble detachment. 183 Superhydrophobic porous copper surfaces have also enabled higher heat transfer coefficients and examination of effects of subcooling have been conducted. 184 The presence of numerous cavities and interconnected pores helps prevents ooding. Superhydrophobic surfaces also make it difficult for bubbles to depart resulting in virtually no change in ow regime throughout the operating conditions.

Effect of micro/nanostructure wickability on ow boiling
The balance of capillary pressure and permeability has been shown to be of critical importance in wick structure development. When the pressure drop of wicked liquid is greater than the capillary pressure, liquid supply to these structures is limited and deteriorates heat transfer. To overcome this limitation, gradient wick structures are designed integrating both, large pore sizes to enhance permeability and small pore sizes to enhance capillarity. 185 These gradient wick structures were found to outperform homogenous wick channels, solid n channels and plain copper surfaces due to the resultant enhanced evaporation. More wicked inow was observed at higher mass uxes owing to higher far eld pressures leading to higher HTCs. It should be noted however that a high degree of turbulence in annular ow could lead to the unintended consequence of earlier onset of dry-out for structured surfaces and thereby potentially lead to lower averaged heat transfer coefficients across the vapor quality range. This is particularly true for larger diameter tubes where the effects of shear force and gravity dominate over surface tension, unlike the case for mini/microchannels. 119

Structure durability
While durability issues for micro/nanostructured surfaces pose limitations to their eventual applicability for industrial processes, 186 few ow boiling studies exist which address this area of concern. Recently, microstructured aluminum surfaces demonstrating up to 270% enhancement have displayed good preliminary durability with the structured surface displaying negligible variation in heat transfer/SEM studies aer 28 days. 187 Overall, more work needs to be done in this regard with long term durability tests focused on variation of operating parameters and channel sizes.

Condensation
Conventional metallic surfaces suffer from limited heat transfer performance due to condensate accumulation from lmwise condensation (Fig. 10A-I). 18 The keys to enhancing condensation are prevention of condensate lm formation and reduction of condensate droplet departure size. 188 The condensation droplet nucleation density and rate is dependent on the intrinsic wettability of a surface. 189,190 Hence, nucleation density is higher on hydrophilic surface compared to hydrophobic surface of lower surface energy. 190 The nucleation radius of condensate droplets is in the nanometer scale and as a result does not depend on the micro or nanostructures of the surface. [191][192][193] Early approaches by researchers to enhance condensation included development of low surface energy promoter coatings to enable dropwise condensation instead of lmwise condensation. 21 Low surface energy coatings enable dropwise condensation by preventing condensate lm formation due to reduced nucleation density combined with efficient continuous droplet shedding (Fig. 10A-II). As a result, dropwise condensation can enable up to an order of magnitude increase in condensation heat transfer. 14

Rational design of micro and nanostructures for enhanced quiescent condensation
In the last decade there has been increased interest in the development of various micro/nanostructured superhydrophobic surfaces to achieve jumping droplet condensation of steam. 194 Jumping droplet condensation on superhydrophobic surfaces (Fig. 10A-III) have been reported to enable up to an order of magnitude enhancement in condensation HTC when compared to dropwise condensation on a smooth hydrophobic surface. 18,195 The larger enhancement of condensation HTC is due to removal of condensate droplets at diameters that are orders of magnitude smaller (<100 mm) when compared to gravity-induced shedding (capillary length, 2.7 mm for water) during dropwise condensation. 196,197 Recent advancements in superhydrophobic surface development have focused on fabrication techniques for implementing optimized structure capable of preventing condensate ooding at extreme conditions such as very high surface subcooling temperatures, and higher vapor supersaturation conditions (Fig. 10). 18,200,201 Jumping droplet condensation performance depends largely on the nanostructure shape, size, orientation, and density. 201,203 For the development of optimized micro and nanostructured surfaces researchers have reported methods such as machining, 204 sandblasting, 205 laser ablation, 206 thermal 207 or chemical oxidation, 18,208,209 chemical etching, 210,211 jet electrolyte micromachining, 212 photolithography, 205 nanoimprint lithography, 213 dry reactive ion etching, 214 electrodeposition 203 etc. However, majority of these micro and nano structure fabrication methods are complex, not scalable, not suitable for large scale industrial application, and are only limited to substrate materials such as silicon which are not commonly used for industrial condenser. Researchers have reported many micro and nanoscale oxide or etched structures that are capable of exhibiting jumping droplet condensation at lower surface subcooling and at low supersaturation conditions. Some of these structures are knifelike nanostructures, 215 nanograss, 199 nanowires, 216 hierarchical-porous nanostructures, 203 nanocones, 217 ribbed nanoneedles, 218 and platelet like nanostructures 201 fabricated on common substrate materials such as silicon, copper, and aluminum (Fig. 10B). Copper oxide nanostructured surfaces continue to be the mostly widely studied surface mainly due to its simplicity and low cost of fabrication. 215 A recent review focusing on micro and nanostructures developed solely for condensation applications provides a detailed summary of past studies with relevant performance parameters. 194 Many of the developed surface structures (i.e., single-tier knifelike copper oxide nanostructures, plate like boehmite nanostructures, etched aluminum microstructures, copper nanowires) suffer from interstructure condensation induced ooding at higher subcooling, vapor pressure, and supersaturation condition (S = P v /P sat ) (Fig. 11A-D). 193,201 Hence, recent studies have focused on the development of rationally designed micro and nanostructures that can prevent such interstructure ooding and exhibit sustainable jumping droplet condensation. For example, studies have reported that fabrication of cellular nanostructures ( Fig. 12A) that are capable of conning the condensate droplets within cells preventing lateral spreading induced ooding and as a result can exhibit jumping droplet condensation at higher subcooling and supersaturation condition. 210 Furthermore, recent studies have shown that addition of multi-tier nanostructures or hierarchical structures on top off such structures can provide anti-ooding superhydrophobic surfaces that can sustain jumping droplet condensation at very high supersaturation conditions (Fig. 12B). 201 In other work electrodeposition was utilized for fabricating hierarchical honeycomb-like structures on copper surface (Fig. 12C). 203 The resultant micro and nano structured copper surface exhibited sustainable jumping droplet condition at higher subcooling temperature compared to smooth hydrophobic surfaces (Fig. 12D). Comparison of the jumping droplet condensation HTC of multi-tier cellular nanostructured surface (AM-EB) with previously reported superhydrophobic surfaces i.e., CuO nanostructures, 18 Cu hierarchical nanostructures, 219 Cu nanowire, 200 3D Cu nanowire, 195 Cu nanocone, 217 Cu nanograss, 199 Si nanowire, 202 Si micro/nanostructures, 220 and conventional Al nanostructures, 201 shows its signicantly improved performance at higher subcooling temperatures (Fig. 12E).
Recent study has shown that synergistic combination of micro/nanostructured roughness with divergent microcavities of a hierarchically structured surface enables enhanced condensation due to hierarchical condensation mechanism (Fig. 13A). 221 During hierarchical condensation large Cassie Baxter state droplets suspended on tops of microstructures act as sinks and enables frequent removal of the shaded droplets ( Fig. 13A and B). As a result, such structure can prevent progressive ooding, and enable higher overall heat ux than an equivalent jumping-droplet-condensation on single-tier nanostructured surface. Besides droplet coalescence induced jumping droplet on a superhydrophobic surface, researchers have recently demonstrated superhydrophobic-groovemediated single droplet jumping (Fig. 13C) during condensation and particle-droplet coalescence induced droplet selftransport which can further facilitate condensate droplet removal. [222][223][224][225] Researchers have also demonstrated electric-eld-enhanced condensation (Fig. 13D) where it was shown that an external electric eld can be applied to prevent the return of the positively charged jumping droplets resulting in a 50% higher overall condensation heat transfer coefficient compared to that on a jumping-droplet surface with no applied eld for low supersaturations (<1.12). 226-229

Low surface tension liquid condensation enhancement
In case of low surface tension liquid condensation, regular micro and nanostructured superhydrophobic or omniphobic surfaces suffer from interstructure condensation induced ooding. 192,230 Studies have shown that it is possible to create reentrant structure geometry that can maintain air pockets within structures, exhibit omniphobicity without any chemical modication by suspending the liquid on top of the structures at Cassie wetting state, and can repel low surface tension liquids (Fig. 14A). 231,232 However, researchers have experimentally shown that nucleating condensate droplets of any liquid can condense within the reentrant microstructures resulting in condensate induced ooding (Fig. 14A-III). 192 Furthermore, super-repellant doubly reentrant structured surface which can repel extremely-low-energy liquids such as uorinated solvents (i.e.,FC-72) are unable to withstand condensate induced ooding as it has no defense against condensate nucleating inside the cavities. 233 Recent study has shown that condensationresistant omniphobic structured surface is required to have a reentrant cavity structure which can prevent Wenzel state condensate droplets from propagating and the pitch of the structure should be less than the nucleation spacing to prevent nucleation from occurring within every cavity of the surface (Fig. 14B). 192 However, fabrication of such reentrant structures is highly expensive, not scalable and not practical for large scale condenser application. Furthermore, long term sustainable condensation of low surface tension liquids on reentrant cavity structured surfaces are yet to be reported. Very few surface modication techniques have succeeded in achieving scalable and sustainable dropwise condensation of low surface tension liquids. [234][235][236] Studies on lubricant infused structured surfaces (LIS) have introduced the methodology of modifying micro and nanostructured surfaces with lubricant infusion for enabling enhanced condensation of liquids. 230,[237][238][239] Lubricant infused nanostructured surfaces have successfully been implemented to achieve stable dropwise condensation of toluene, ethanol, hexane, and pentane which are low surface tension uids (Fig. 14C-F). 234,[240][241][242] The studies showed that LIS enhances HTC by 200%, 200%, and 450% for condensation of ethanol, hexane, and toluene, respectively when compared to lmwise condensation on an untreated surface. Researchers have shown it is possible to further reduce the condensate droplet departure size and increase the condensation rate on a LIS by introducing vibrational actuation. 243 However, LISs have limited lifespan depending on choice of lubricant, lubricant condensate miscibility, condensate cloaking by lubricant, and lubricant drainage over time. [244][245][246][247] Until now, the longest reported lifetime of LIS is more than 8 months of continuous ethanol condensation and 45 days for water condensation (Fig. 14G) for CuO nanostructured surfaces infused with high viscosity Krytox 16256 lubricant (5216 mPa s) 171 before transitioning to lmwise condensation due to lubricant depletion. To alleviate the limitation of LIS due to oil depletion during condensation applications recent studies have proposed complex and expensive mechanisms i.e., lubricant replenishment through brushing of the surface. 248 Due to these limitations of LIS, to achieve dropwise condensation of low surface tension liquids researchers have resorted to implementation of low surface energy and low hysteresis coating i.e., iCVD and polydimethylsiloxane-silane coated smooth surfaces. 235,236 Recently researchers have also investigated hydrophobic polymer (Teon AF) infused nanostructured porous surface for condensation application, known as PIPS (Fig. 14H-J). The PIPS was shown to be signicantly more durable than a Teon coated surface, delivering 700% improvement over an uncoated surface for 200 days. 249 However, PIPS have only been studied for condensation of steam (Fig. 14J) and its potential for low surface tension liquids condensation is yet to be investigated.

Hybrid wettability surfaces for enhanced dropwise condensation
Recent advancements have also focused on development of nature inspired biphilic or hybrid wettability surfaces which consist of a combination of different wettability regions (i.e., superhydrophilic, hydrophilic, hydrophobic, and superhydrophobic). 250 Hybrid wettability surfaces have been shown to enhance condensation due to increased preferential condensate nucleation at the hydrophilic regions as condensate nucleation on hydrophobic surfaces requires a higher degree of supersaturation. 191,251 Furthermore, unlike on a completely hydrophilic surface, the presence of the hydrophobic region a hybrid surface can enhance droplet shedding and prevents condensate ooding at higher subcooling temperatures. 250,252 To enhance condensation heat transfer and to prevent condensate ooding researchers have investigated many variations of hybrid surfaces with varying combination of surface wettability, i.e., hydrophobic-hydrophilic, 253 superhydrophilichydrophobic, 254 superhydrophobic-hydrophilic 255,256 and superhydrophilic-superhydrophobic. 257 Furthermore, varying designs of hybrid patterned surfaces (i.e., nature inspired patterns, 250 branching topology, 258 geometrical shapes, 259 randomly distributed micro 250 and nanopatterns 255 ) and varying geometries of patterns (i.e., grooved, 254 wedge shaped, 257 straight, 205 square, 216 circular, 260 elliptical, 259 diamond 259 ) have also been investigated in recent years (Fig. 15).
Studies have shown that hydrophilic-hydrophobic nned surface can achieve superior performance with ∼40 kW m −2 K −1 condensation HTC in pure vapor conditions, 253 while hydrophilic-superhydrophilic nned surface gives the best performance in the presence of non-condensable gases. By implementing straight and circular hybrid patterns on copper tubes researchers were able to achieve maximum condensation HTC of ∼85 kW m −2 K −1 which is 1.8 times the HTC of complete dropwise condensation at 9 K subcooling. 205 However, implementing optimized circular patterns (Fig. 15A) yielded 50% higher HTC when compared to complete dropwise condensation at 9 K subcooling. 260 In comparison, diamond shaped patterns (Fig. 15A) can provide 60% higher condensation HTC when compared to a complete hydrophobic surface and also have been shown to outperform circle and ellipse shaped patterns. 259 These studies explored the effect of circular, parallel condensate on the hydrophilic spots. 256   straight, and diamond shaped patterns of varying size and spacing where the patterns were more hydrophobic than the background and determined the optimized design to maximize the wettability contrast enabled condensate removal (Fig. 15B). A recent study has shown that a 3D hybrid surface (Fig. 15C), consisting of hydrophilic microchannels in superhydrophobic Si nanowire surface, can achieve maximum condensation HTC of ∼53 kW m −2 K −1 at ∼8 K subcooling. 214 The 3D hybrid architecture prevents surface ooding at higher subcooling by conning the liquid-lm thickness and enabling self-removal of liquid bridges formed on the surface (Fig. 15C). Studies have shown that implementation of constructal-like hybrid wettability patterns which presents a branching topology makes the condensate convergence and departing process more efficient, increasing condensate collection by 30%. 258 Researchers have shown that hybrid wettability patterns at micro and nanoscale can enhance condensation heat transfer performance and prevent condensate induced ooding of superhydrophobic surfaces at higher supersaturation conditions ( Fig. 15D-F). 252,255 For example, microscale hydrophilic patterns can be utilized to impart spatial order of condensate through preferential nucleation and self-organization of coalescing droplets at high supersaturations ( Fig. 15D and E). As a result, microscale hydrophilic patterned superhydrophobic surfaces have enhanced condensation heat transfer without condensate induced ooding when compared to ooded superhydrophobic surfaces at high supersaturations (Fig. 15E). 252 Similarly, biphilic nanomorphology surfaces implemented on horizontal tube surfaces (Fig. 15F) have been shown to prevent condensate ooding by sustaining coalescence, droplet jumping and condensate self-removal. 255 Thus biphilic nanomorphology enabled hybrid surface can achieve condensation enhancements resulting in 123% higher condensate collection at 60% relative humidity when compared with uncoated surfaces.
Hybrid surfaces consisting of wedge-shaped superhydrophilic patterns on superhydrophobic backgrounds (Fig. 15G) can transfer condensate from the dropwise region to the lmwise region facilitating droplet departure and thus enhancing condensation heat transfer by 30% when compared to a uniform superhydrophobic surface. 257 Most of the literature on hybrid surfaces incorporates visualization studies to investigate mechanisms for sustaining dropwise condensation, condensate ooding prevention and enhanced condensation. The majority of these studies have been conducted in the presence of varying degrees of non-condensable gases which makes the acquired heat transfer performance of these surfaces incomparable. The scarcity of comparable condensation performance results of these hybrid surfaces makes it imperative to conduct further rigorous and standardized experimental studies in pure vapor environments to achieve a better understanding of the efficacy of hybrid wettability surfaces.

Nanostructuring of additively manufactured surfaces for enhanced condensation
Additive manufacturing (AM) of metal heat exchangers has gained signicant popularity in heat transfer and thermal management applications due to its design exibility and ability to manufacture complex compact components, not achievable by conventional manufacturing techniques. [261][262][263] Over the last decade researchers have shown implementation of additive manufacturing for the development of air-cooled heat exchangers, 264 liquid cooled heat exchangers, 262 porous ultracompact heat exchangers, 261 three-dimensional pin ns, 265 and tubes with genetically optimized internal ns 263 for enhanced heat transfer performance (Fig. 16A-D).
Recent studies have focused on synergistic combination of micro and nanostructuring of AM metal surfaces along with its design exibility to further enhance condensation performance. 201,210,266 Due to signicantly different elemental composition of AM materials along with the AM laser melting and rapid solidication processes, as fabricated AM surfaces consist of unique sub-grain structures compared to conventionally manufactured metal surfaces. [267][268][269] Researchers have demonstrated that these unique sub-grains have unveiled the possibility of generating unique micro and nanostructures by varying heat and chemical treatment of AM surfaces. For example, a recent study has demonstrated that for AlSi10Mg AM alloy, different combination of post processing methodology utilizing optimized heat treatment and chemical etching can yield unique micro/nanostructured surfaces (Fig. 16E). 210 These nanostructures i.e., nanocells, nanocell with nanobumps and microsteps can be utilized to develop superhydrophobic surfaces with varying degrees of droplet adhesion and condensate droplet repellency. The study compared the jumping droplet condensation performance of a conventional boehmite nanostructured surface with an AM non-heat treated etched (nanocells) and heat-treated etched (nanocell with nanobumps) AM surface. The structures with second-tier nanobumps generated by heat treatment at 300°C followed by chemical etching showed the best performance exhibiting jumping droplet condensation with condensation HTC of ∼85 kW m −2 K −1 even at high supersaturation of S = 1.05. In comparison, the single tier nanocellular structured AM surface and the single tier boehmite nanostructured conventional aluminum surface failed to sustain jumping droplet condensation in similar conditions. The study showed that the secondtier cellular structured AM surfaces can sustain jumping droplet condensation by preventing lateral spreading of condensate droplets at higher nucleation and growth rates. This was further veried by another study where condensation performance of three large scale AM tubes consisting of single tier boehmite (AM-B), single tier nanocells (AM-E), two tier nanocells with boehmite (AM-EB) were compared (Fig. 16F). 201 Unlike the single-tier nanostructured surfaces, two-tier nanostructured AM-EB surface sustained jumping droplet condensation even at high supersaturation of S = 1.8 at 7.4 kPa pure vapor pressure and showed the highest condensation HTC of ∼65 kW m −2 K −1 compared to the other surfaces and ∼6 times higher than lmwise condensation. This enhanced condensation was further shown on an AM two-tier nanostructured compact monolithic heat exchanger (Fig. 16G) proving the applicability of scalable nanostructuring method on unconventional AM heat exchangers. Internal ow convective condensation can be described as condensation where a pure vapor or liquid-vapor mixture at some prescribed quality enters the test section and heat is removed from the walls allowing the vapor or mixture to condense. The majority of prior research that applies micro and nanostructuring to condenser surfaces has only focused on external quiescent condensation. Few studies have explored the implementation of these structures for internal ow convective condensation.
Internal ow condensation enhancements are of great interest, as it has the potential to increase the efficiency in many applications i.e., air-cooled coils for refrigeration, 270 heat exchangers for thermosyphons used in electronics thermal management, 271 and steam condensers in power plants. 272 Internally functionalized copper tubes fabricated with infusion of a metal powder slurry and sintering aerwards (Fig. 17A) were shown to enable a 33% to 45% improvement in ow condensation HTC of R410a when compared to smooth tubes. 201 For condensation heat transfer of R141b, implementation of copper oxide nanostructures was able to provide a 16.67% enhancement compared to the original copper channel with contact angle of 12.8°, which was attributed to the capillary force accelerating the condensate liquid when the mass ux was less than 400 kg (m 2 s) −1 . 273 For steam condensation applications, a tube with a metal foam internal surface (Fig. 17B) was fabricated followed by surface oxidation and chemical modication with immersion in hydrochloric acid. 274 The result is a metal foam with hydrophobic characteristics which can range from 10 PPI to 20 PPI. The study showed aer hydrophobic coating metal foam tube could increase the ow condensation heat transfer performance and reduce the pressure drop compared to untreated metal foam tube.
A recent study has characterized the heat transfer and pressure drop performance of CuO nanostructured superhydrophobic condenser tube during internal ow condensation (Fig. 17C). 149 The experimental results showed superhydrophobic surface had the highest HTC (z68 kW m −2 K −1 ) at a lower heat ux (z50 kW m −2 ). At a higher heat ux superhydrophobic surface transitioned to ooded condensation mode and exhibited HTC similar to that of lmwise condensation (z26 kW m −2 K −1 ). However, dropwise condensation on hydrophobic surface reached maximum HTC (z65 kW m −2 K −1 ) above z 250 kW m −2 heat ux. The study also showed that for all the tubes the HTC increased with inlet vapor velocity and superhydrophobic surface exhibited lower pressure drop compared to hydrophobic and hydrophilic tubes. Another study investigated the condensation heat transfer performance of Cu(OH) 2 nanowires under the stringent ow condensation conditions of saturated vapor at 110°C saturation temperature up to a high heat ux ∼600 kW m −2 at 10 K subcooling and 18 m s −1 vapor velocity (Fig. 17D). 275 The study showed that with an increase in the vapor velocity, the size of the departing droplets becomes smaller and enhances heat transfer performance on the superhydrophobic surface. Furthermore, the superhydrophobic surface showed enhanced condensation up to 5 days before nanostructure degradation resulting in transition of condensation mode to lm condensation on the 6th day. Previous studies on external quiescent condensation have also reported similar degradation of structured surface where collapse and breakage of nanograss like structures deteriorated the heat transfer performance during long-term application. 199 Further future work should be conducted in the future to develop robust and durable nanostructures for long term ow condensation application and to acquire a better understanding of the internal condensation mechanism. Investigations involving better visualizations can offer additional insights into temporal transition from jumping droplet condensation to lmwise condensation during internal forced convective vapor ow. Superhydrophobic surfaces can degrade during long term condensation due to degradation of structures or delamination of low energy coating. 275,276 To address this concern, recent studies have focused on the development of robust micro and nano structures as well as development of durable low energy coatings with highly adhesive interfaces. 194,276 Micro and nanostructures enabling jumping droplet condensation during internal ow condensation has been looked at in more details from a modeling perspective. Comprehensive modeling of jumping droplet condensation during internal ow condensation has been utilized to further elucidate the effects of droplet size, heat ux, droplet jumping location, vapor mass ux and pipe radius on droplet trajectory, heat transfer performance and pressure drop. 277

Machine learning methods for boiling and condensation
Recently, there has been a steady rise in the use of machine learning (ML) techniques for prediction and characterization of complex two-phase heat transfer problems such as condensation and boiling. [279][280][281][282][283] These techniques have shown a promising pathway for enhancing the performance of predictive models in these complex physical phenomena and have also helped with better feature extraction and understanding of the underlying physics. Many studies have focused on using ML models to substitute the empirical or semi-empirical correlations developed for pressure drop and heat transfer estimation of internal condensation and boiling. Supervised ML models such as Articial Neural Network (ANN), Decision Tree, Random Forest, K-nearest neighbors regression (KNN-regression), Adaptive boosting (AdaBoost), and Support Vector Machine (SVM) have been developed as regression models to estimate Heat transfer coefficient dependence on the wall subcooling during DWC on a superhydrophobic copper sample at three different vapor velocities. 275 (1), where N is the number of data points, h exp and h pred are the experimentally measured and predicted heat transfer coefficients.
However, the model accuracy diminished slightly and drastically when testing on unseen data with working uid included in the training dataset and unseen data with working uid out of the training dataset, respectively. These results demonstrate that although the model was doing a good job interpolating from the data and attaining higher accuracy than empirical correlations, it failed in extrapolation on unseen working uids with different properties. The same methodology was used to build 4 models of ANN, AdaBoost, Gradient Boosting, and Random Forest over 4882 data points from 37 sources to predict internal ow condensation heat transfer in mini/microchannels with ANN showing the lowest MAE (6.8%) when testing on training dataset. 285 This value is almost 20% lower than the MAE of the state-of-the-art correlation developed for ow condensation HTC. However, the model performed poorly on unseen data where the uid information was not available in the training dataset and MAE increased to 77%, suggesting strong dependency to prior data. This is due to the lack of understanding of the underlying physics behind these models, making them only excellent regression models. Visual data could provide more insights into phase change problems which has led to development of more universal models. However, recording visual data from ow boiling and condensation systems is inherently challenging, and data is limited.
Visual data are more prevalent in pool boiling and external condensation processes. Recently, more studies have focused on developing deep learning based models using visual data for pool boiling heat ux estimation. [290][291][292] One such example was data collection from pool boiling experiments using a commercialized DSLR camera and training of a convolutional neural network (CNN) to predict heat ux in nucleate boiling regime. 290 The CNN model was able to capture bubble morphology which encoded extensive information about the heat ux. The drawback of this model was the single geometry conguration of the data used in training which lessened model universality. In another study, a high-speed camera was used to acquire 2000 frames per second (fps) images from pool boiling experiments to develop a physics-informed learning framework 8 by combining an image recognition network (VGG16) 293 with a segmentation network (Mask R-CNN). 294 The image recognition network was used for hierarchical image feature extraction and the segmentation network was used to extract physical features such as bubble size and count. The outputs of these networks were passed through another multi-layer perceptron network to attain heat ux during the boiling as the nal output. Their framework successfully predicted the steady-state and transient heat uxes on boiling curve for heat uxes up to 100 W cm −2 .
In addition to the CNN based model developed for pool boiling heat ux estimation, recurrent neural networks could also be used to take into account the boiling process variation with time to better perceive the bubble dynamics and possibly predict the bubble dynamics in future frames which could be used for early detection of boiling crisis. A model developed using a bidirectional long short-term memory (BiLSTM) was able to predict bubble morphologies for pool boiling using the rst few principal components of time-series data which were extracted using principal component analysis (PCA). 295 Every single data consisted of 300 milliseconds (ms) of sequential data, from which the rst 200 ms was used as the input and the next 100 ms as the output and the network was trained to predict the transient behavior of the principal components during the 100 ms period. The dominant frequency and the amplitude of the dominant frequency obtained from Fast Fourier Transform (FFT) of the predicted principal components were shown to be strong indicators of the onset of the boiling crisis. In addition to visual techniques, acoustic techniques have been shown to accurately predict CHF in pool boiling, through an increase in peak frequency on transitioning to CHF. 296 Training of a CNN's with acoustic emissions have also been recently utilized for identication of boiling regimes such as natural convection, nucleate boiling, and transition boiling. 297 Despite the presence of several studies of boiling, visual data along with deep learning models have been less explored for external condensation. A few recent works have however shown great potential in application of these techniques for characterization of external condensation. A vision-based deep learning framework consisting of object detection, tracking, and data processing modules for external condensation images has been recently proposed. 298 Using this framework on condensation visual data, physical descriptors such as droplet growth rate, droplet distribution, and heat ux were extracted. Statistical analysis of the segmented droplet images during condensation on hydrophobic and superhydrophobic at surfaces enabled studying transient measurement of heat ux and the effects of single droplet heat transfer rate and the droplet size distribution on the total heat transfer rate from the surface. In another study, a methodology was proposed to measure condensation heat ux (with uncertainty less than 10%) using condensation videos by detecting and counting falling droplets from condensing tubes, 299 using an object detection network called EfficientDet. 300 By eliminating the need for temperature sensors, the proposed method achieved lower uncertainty compared to the conventional experimental methods. Furthermore, successful application of this methodology enabled local heat transfer measurements on tubes having axially varying surface properties resulting in different heat transfer rates at each location. A summary of recent studies focusing on learning-based models for condensation and boiling is shown in Table 1. Most studies have focused on development of supervised models to replace the empirical correlation and have shown strong capability for regression on training datasets. However, these lack generalizability for extrapolative purposes and suffer from low explainability. 280 Intelligent-vision based methods could be used to extract meaningful and physical features from complex pool boiling and external condensation studies. In addition to extracting features, novel, low-cost, and robust characterization methods could also be developed using stateof-the-art deep learning algorithms along with visual data to replace complex and expensive experimental methods. These advanced methodologies have been mainly limited to pool boiling and external condensation due to higher visual data availability for these processes. With recent advances in datadriven models and learning-based computer vision algorithms and the recent deployments of these methods for thermouidic sciences, application of these techniques to structured surface phase-change processes can greatly improve predictive ability and aid in future experimental design.

Conclusions and outlook
This paper presents a comprehensive review of the recent progress in the development of micro/nanostructured surfaces for enhanced boiling and condensation. Review of recent studies shows the development of numerous surface nanostructures for minimizing condensate droplet departure size by achieving enhanced jumping droplet condensation or enhanced droplet shedding on lubricant infused surfaces. Despite development of a plethora (>1000) micro and nanostructures, only a few recent studies have explored surface nanostructures that can exhibit sustainable jumping droplet condensation at higher supersaturation and subcooling conditions. Recent studies have shown implementation of nanostructure morphology which facilitates condensate droplet nucleation within interstructure spacing preventing excessive lateral spreading of the condensate enabling jumping droplet condensation even at higher supersaturation and subcooling. However, when it comes to enhanced condensation of low surface tension liquids, recent studies have shown that the nanostructure itself cannot sustain dropwise condensation due to interstructure ooding by nanoscale condensate droplets and requires infusion with low energy lubricants to enable the shedding of the condensate droplets from the low hysteresis lubricant surface. Many studies have focused on condensation durability of these micro and nanostructured surfaces and proposed rational designs for long-term condensation considering three aspects which includes mechanical robustness of the structures, durability of the low energy coating, and oil retention capability of lubricant infused surfaces.
When it comes to boiling enhancement, this review elucidated the role of structures in promoting bubble nucleation, preventing dry out and prolonging wicking anti-degeneration. Apart from the signicant enhancements in HTC and CHF achieved by structured surfaces, the recent development of state-of-art in situ optical visualization techniques also enables the identication of previously unidentied three-phase contact line dynamics, advancing the fundamental understanding of the complex thermal transport process and bubble-structure interaction mechanisms. While many existing works focus on the understanding of bubble generation mechanisms on structures and their thermal performance, equally important are their robustness, durability and anti-degeneration characteristics required to sustain long-term (>5 years) operation. A recent study has demonstrated good anti-degeneration of structures through year-long wickability and boiling heat transfer measurements in water, however more studies are needed for other structures and working uids.
Highly scalable, shape conformal and cost-effective structuring strategies are important criteria for industrial implementation. While structuring methods such as thermal oxidation, wet etching and electrochemical deposition have demonstrated these attributes, they are implemented only on copper and aluminum alloys. Development of similar structuring methods for other metals such as stainless steel and titanium are important to improve the efficiencies of condensers, boilers and evaporators facilities requiring good corrosion resistance or high temperature operations.
While most studies focus on the development of new and previously-unpublished structure morphologies, structuring strategies that can be implemented on internal surfaces and that are able to promote boiling or condensation, are compatible and durable with low surface tension uids such as refrigerant and dielectric uids, remain challenging and require further study. If successful, the development of these structures will have signicant implications to a number of industries.
Studies have shown that optimization of structure designs across multitude of length scales opens the door to further enhancement in boiling and condensation performance. Recent studies have demonstrated this design methodology through the generation of structures consisting of nanopores, micro-dendrites and micropores (hundreds of nanometers to tens of micrometers) to form three-tier hierarchical surfaces achieving approximately 3X CHF enhancements in pool boiling. In future, it would be interesting to further explore the design space by combining macrometric features of millimeter lengthscale with the micro-and nanostructures. Such optimization of strategies can be useful in regulating the vapor escape pathway with the appropriate placement of macro-ns while utilizing the micro/nanostructures as preferential bubble nucleation sites. Similarly, hierarchically nanostructured surfaces have been shown to provide higher condensation heat transfer enhancement and exhibit sustainable jumping droplet condensation even at extreme conditions. More work directed at comparison of microscale and nanoscale structures for specic applications such as condensation and boiling heat transfer enhancement needs to be performed to better summarize the effects of the two length scales.
Metal AM techniques have received signicant attention as they possess great versatility to manufacture complex functional parts with complex macro-geometries and intricate millimeter or sub-millimeter features. Due to the unique layerby-layer fabrication process, recent studies have demonstrated the potential of generating new and tunable micro and nanoarchitectures on AM alloys previously not found on conventionally produced metals. Although past investigations have demonstrated the exceptional performance of these structures in droplet repellency, condensation and anti-icing, their wicking and boiling characteristics remain unknown, and would be interesting to study in future.
Finally, much work has been devoted over the past few years to the development of data-driven models and learning-based computer vision algorithms in the eld of thermouidic sciences. Although a plethora of ML studies have been conducted for predicting heat transfer performance of conventional surfaces, our review shows there is a lack of machine learning based studies for evaluating micro and nanostructured surface performance. Application of these techniques to structured surface enabled phase-change processes can greatly improve predictive ability and aid in future experimental designs given the many choices of surface structures available.

Conflicts of interest
There are no conicts to declare.